The 1821 painting was covered with an image the activists called “an apocalyptic vision of the future”, as Hunt and Lazarus glued their hands to the frame.
Hunt and Lazarus have now been charged with criminal damage after a Metropolitan Police investigation, and are due to appear at Westminster magistrates court on Wednesday.
According to the charge, they are accused of “damaging The Hay Wain painting and frame to the value of £1081.49 belonging to The National Gallery”.
The protest, at around 2.15pm, happened in front of a class of school children, and forced the evacuation of the gallery room where the famous painting hangs.
Psychology student Hunt, from Brighton, and music student Lazarus, from Wiltshire, were wearing t-shirts bearing the Just Stop Oil logo as they stepped over the rope barrier which guards the painting.
Constable’s masterpiece depicts a rural Suffolk scene of a wagon returning to the fields across a shallow ford for another load.
It was covered by the protestors with an image of an old car dumped in front of the Mill and the Hay Wain cart carrying an old washing machine.
After the incident, the National Gallery said “minor damage” had been caused to the frame, as well as “disruption to the surface of the varnish on the painting”.
Hunt and Lazarus are accused of “intending to destroy or damage” the painting and frame, or “being reckless as to whether such property would be destroyed or damaged”.